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A Hilbert Space Approach to the Collatz Conjecture Problem Using an Infinite-Dimensional Operator

Year: 2024

Type: article

Abstract: This paper explores an approach to the Collatz conjecture through the lens of functional analysis. We construct an infinite-dimensional operator T on the l^2 Hilbert space, where the basis vectors represent natural numbers. By analyzing the spectral properties of T, we provide insights into the conjecture's behavior. The compactness of T^(inf) suggests a finite-dimensional limit for the image of the operator under infinite applications, mapping the space onto a subspace characterized by the numbers 1, 2, and 4.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.14017698

Author: Kartomin, Nikita

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6911673108

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